mathsurgery - Edexcel module 2-3

nit 2 Module 2-3 of 20

Contents: Laws of Indices	Time: 1 – 4 hours
SPECIFICATION REFERENCE
N e, f	Use index notation and index laws for multiplication and division with integer powers
N f	Use index laws to simplify and calculate the value of numerical expressions involving multiplication and division of integers, fractional and negative powers and powers of a power
N f	Use inverse operations involving
N f	Recall the fact that n0= 1 and n–1= for positive integers n, the corresponding rule for negative integers, = √n and = for any positive number n
PRIOR KNOWLEDGE
Knowledge of squares, square roots, cubes and cube roots
OBJECTIVES Lesson plans
Use index rules to simplify and calculate numerical expressions involving powers, eg (23 ´ 25) ¸ 24, 40, (1.4, 5.1, 5.3) Know that, eg x = Þ x3= 8 (5.1, 5.3)
DIFFERENTIATION & EXTENSION
Use index rules to simplify algebraic expressions Treat index rules as formulae (state which rule is being at each stage in a calculation)
NOTES
Use a simple division example to illustrate how zero and negative indices occur, eg 33 ÷ 33 for zero index and 33 ÷ 34 for a negative index

Properties of numbers & laws of indices

N2

t 2 Module 2-2 of 20

Contents: Factors and multiples	Time: 1 – 4 hours
SPECIFICATION REFERENCE
N c	Understand even, odd and prime numbers
N c	Find factors and multiples of numbers
N d	Find squares and cubes of numbers, and find square roots and cube roots of numbers
N c	Find Highest Common Factor (HCF), Lowest Common Multiple (LCM) and prime factor decomposition
PRIOR KNOWLEDGE
Number complements to 10 and multiplication/division facts Use a number line to show how numbers relate to each other Recognise basic number patterns Experience of classifying integers
OBJECTIVES Lesson plans
Find: squares, cubes, square roots, cube roots of numbers, without a calculator (1.2) Understand odd and even numbers, and prime numbers (assumed) Find the HCF and the LCM of numbers (1.1) Write a number as a product of its prime factors, eg 108 = 22 ´ 33 (1.1)
DIFFERENTIATION & EXTENSION
Calculator exercise to check factors of larger numbers Further work on indices to include negative and/or fractional indices (intro to next section) Use prime factors to find LCM Use a number square to find primes (Sieve of Eratosthenes) Calculator exercise to find squares, cubes and square roots of larger numbers (using trial and improvement)
NOTES
This topic can easily be reinforced by using it as material for starters and plenaries Calculators are only to be used when it is appropriate Encourage students to learn square, cube, prime and common roots as Unit 2 is a non-calculator examination